Model investigations

4.1 Methods and model description

The aim of the model was the estimation of pre-breeding survival rate in two populations of Lesser Spotted Woodpeckers. To achieve this objective, we constructed an individual-based stochastic model simulating the population dynamics. Model construction was progressed in four steps. (i) First, we constructed a general framework for the model with a set of rules describing the processes within the population dynamic (e.g. survival). These processes occur with certain probabilities described by parameters. (ii) In the second step, we calculated values for all included parameters based on empirical investigations. Since we wanted to compare pre-breeding survival in two populations, we created two different scenarios, one based on the field investigations in Germany, the other on the investigations in Sweden. (iii) In the third step, independent empirical data that might be useful as pattern were selected and analysed. (iv) In the last step, simulations were run varying the value of the missing parameter systematically. That way the value was detected where model output matches best with all selected empirical pattern. These four steps are described below in detail.

4.1.1 (i) General framework and model rules

Structure of the model is individual-based, i.e. birds are followed individually between fledging and death and the population is seen as the assemblage of all individuals. All individuals have the attributes age, sex, mating status (newly paired, old paired and unpaired), breeding start (early and late) as well as an identification number. When individuals are paired, all attributes of the mate are known.

Simulations have a yearly time step, beginning in spring and including the processes of mating, reproduction and deaths (see Fig. 1). Some attributes (e.g. mating status) are set every time step, following model rules (e.g. when the partner dies, the individual becomes “unpaired”).

Based on the knowledge of the species’ autecology, we described the processes within the individual’s life cycles in rules. These processes occur with certain probabilities, which are not fixed in the model rules but described by parameters (see Table 1). Therefore, the following rules are consistent for any Lesser Spotted Woodpecker population and scenarios for particular populations can be developed by a specification of the model parameters (see (ii)). Empirical background and derived model rules are described as follows:

Model rules

Mating Male and female Lesser Spotted Woodpeckers start to breed in their first year after fledging and form usually lifelong pair bonds, although divorce might occur (Glutz von Blotzheim & Bauer 1994; Wiktander et al. 2000, own obs.). Rule 1: If both partners from the previous breeding season are still alive, they establish an old pair. With a minor probability (pDivorce) they split up and mating status becomes unpaired. Unpaired males mate with unpaired females and establish a new pair. If there is no unpaired partner available, the individual remains unpaired.

Chapter III · Model structure

Non breeder: In the Swedish population, some Lesser Spotted Woodpecker pairs did not produce eggs, even though they occupied a territory and built a breeding hole. All those non breeders were

new pairs (Wiktander et al. 2001b). However, this behaviour never appeared in the German

population (own obs.). Rule 2: While old pairs always lay eggs, probability for a new pair not to breed is pNonBreed.

Start of egg laying: Old pairs start earlier with egg laying than new pairs, which has a positive effect on reproductive success (Chapter I; Wiktander et al. 2001a). Rule 3: All old pairs have an early breeding start, while new pairs have an early breeding start with the probability pStartEarly, otherwise their breeding start is late. The breeding start is an attribute that influences the number of young that fledge (see rule 7).

Failure in reproduction: Some pairs fail to reproduce, because eggs do not hatch or both parents desert the nests without obvious reason (Chapter I; Wiktander et al. 2001b). Rule 4: The probability to fail because eggs do not hatch or parents desert the nest after egg laying is for all pairs

pFailure. Additionally, issues described in rule 5 and 6 can cause failure in reproduction.

Nest predation: Most common nest predators are Great Spotted Woodpeckers (Picoides major) and Eurasian jays (Garrulus glandarius) (Chapter I; Wiktander et al. 2001b). Rule 5: Nest predation occurs with the probability pPredation and result in the death of all nestlings.

Mortality during breeding season: If one partner dies during breeding season, the mate leaves the nest and the brood fails (Chapter I; Wiktander et al. 2001b). Rule 6: When an individual dies (probabilities to survive pSurvBreedmale and pSurvBreedfemale) its brood fails and its mate remains unpaired until the next breeding time.

Fledging: Pairs that start early with egg laying produce more fledglings than late broods (Chapter I; Wiktander et al. 2001b). Rule 7: In successful nests, i.e. when parents have survived the breeding season and no predation has occurred, nestlings fledge. The probabilities for a certain number of fledglings were calculated based on empirically observed distribution of brood sizes in the field, divided in early p(x)Fledglingsearly pairs and late broods p(x)Fledglingslate pairs with x indicating the number of fledglings (Table 1). Based on the observed sex ratio of fledglings in the field, the probability for a fledgling to be male is pYoungMale, otherwise it is a female.

Pre-breeding survival: Empirical data about mortality after fledging are missing. Rule 8: Fledglings suffer a certain mortality rate after leaving the nest until they reach their first breeding time. The survival probability (pSurvWinterjuvenile) is unknown and is varied systematically.

Emigration: Adult Lesser Spotted Woodpeckers have a strong site fidelity and stay in the area once they have settled. Emigration appears only in immature individuals (Wiktander 1998). Rule 9: There is a maximum number of territories, i.e. a maximum number of individuals that can exist in the area, given in the parameter carrying capacity. Only if the number of birds is below the carrying capacity, fledglings can stay in the area, otherwise they emigrate. Since adult birds do not emigrate, an occupied territory only becomes available once an individual dies.

Figure 1 Simplified float chart for the Lesser Spotted Woodpecker simulation model. Grey boxes indicate stochastic processes in which the result is determined by a probability and a random number.

Adult survival in non-breeding season: The oldest individual Lesser Spotted Woodpecker of known age reached 10 years (Wiktander pers.comm.). Rule 10: If an individual exceeds maximum age (=10 years), it dies. Otherwise it has the probability of pSurvWintermale and

pSurvWinterfemale to survive.

Ageing: Rule 11: At the end of the simulation year, dead individuals are removed from the population and the age of all individuals is enhanced by one year.

Chapter III · Model structure

In the Lesser Spotted Woodpecker, density dependent effects on reproduction or survival could not been found (Wiktander et al. 2001b). Therefore, parameter values do not change with population densities in the model. However, emigration is density dependent, since fledglings emigrate when all territories are occupied.

Model rules were implemented as a computer program in C++ and simulations were conducted on a common personal computer.

Stochasticity

In natural variable environments, population dynamics are subject to demographic as well as environmental noise (May 1973). To mimic demographic noise, all parameter values shown in Table 1 are interpreted as probabilities (Wichmann et al. 2003). In processes that are supposed to be influenced by environmental changes between years (see Table 1), involved parameter values for the current year were determined at the beginning of each time step by drawing from a normal distribution cut at 0 and 1, based on mean and standard deviation of the empirical data. The drawn value is then interpreted as the probability for the process in the current year and demographic stochasticity acts additionally.

Furthermore, there are non-stochastic parameters, like maximum age, carrying capacity and population size at simulation start.

4.1.2 (ii) Analysis of parameter values

In Table 1, parameters for both scenarios (Germany and Sweden resp.) are shown. The column “quality” in Table 1 gives an estimation on the reliability of the parameter values based on sample sizes (n<=20: +, n>20: ++).

For the unknown parameter pre-breeding survival, we can only assume a realistic range based on theoretical considerations: In birds, survival of juveniles is generally lower than that of adult individuals (Newton 1989; Van der Jeugd & Larsson 1998). Therefore, in the Lesser Spotted Woodpecker we assume maximum pre-breeding survival to be lower than survival rate in adults. The minimum rate of survival in juveniles is the rate of recoveries of local recruit in the study areas.

In the Swedish population, survival rate of yearling birds was 0.63 (males) and 0.45 (females) resp. (Wiktander unpubl.). Therefore, pre-breeding survival rate is supposed to be below 0.45. The proportion of recovered fledglings as local recruits and therefore the lower limit was 6% in Sweden (Wiktander 1998). In the German population, yearling survival rate is not known, but adult survival rate is 0.58 (males) and 0.62 (females) resp. We therefore assume that pre-breeding survival in the German scenario is remarkably lower than 0.58. The lower limit for survival rate is set at 0.20, based on local recoveries (Chapter I).

There is no sex-specific behaviour before the first breeding time and body mass and thus “quality” of fledglings was not different between the sexes (Rossmanith unpubl.). Therefore, we do not distinguish between survival rates of male and female juveniles.

Table 1 Parameter set for the two scenarios. All parameter values for the German scenario are shown in the empirical part of this paper or are based on Chapter I, II, Höntsch unpublished and own observations. For the Swedish scenario, values are based on Wiktander (1998), Wiktander et al. (2000, 2001a, 2001b & 2001c) and Wiktander & Olsson unpublished.

Germany Sweden Description

Stochastic parameters Value Qual. Value Qual. Probability...

pDivorceold pairs 0.03 + 0.034 ++ for old pairs to split up

pNonBreednew pairs (+ s.d.) 0.0+ 0.0 ++ 0.126 + 0.139 ++ for new pairs to lay no eggs

pStartEarlynew pairs 0.46 + 0.49 ++ for new pairs to start early

pFailure 0.03 ++ 0.04 ++ to fail reproduction due to unhatched eggs

pPredation (+ s.d.) 0.16 + 0.02 ++ 0.056+ 0.05 ++ to fail due to predation

pSurvBreedmale pSurvBreedfemale 0.969 0.966 ++ ++ 0.936 0.936 ++ ++

to survive during breeding time

p(x)Fledglings early pairs 0.09 [x=2] 0.33 [x=3] 0.33 [x=4] 0.25 [x=5] + 0.02 [x=2] 0.07 [x=3] 0.14 [x=4] 0.35 [x=5] 0.37 [x=6] 0.05 [x=7]

++ for successful pairs with early breeding start to produce x fledglings

p(x)Fledglings late pairs 0.20 [x=1] 0.20 [x=2] 0.40 [x=3] 0.00 [x=4] 0.20 [x=5] + 0.09 [x=1] 0.13 [x=2] 0.17 [x=3] 0.35 [x=4] 0.04 [x=5] 0.17 [x=6] 0.05 [x=7]

++ for successful pairs with late breeding start to produce x fledglings

pYoungMale 0.54 ++ 0.446 ++ to become male at birth

pSurvWintermale (+ s.d.) pSurvWinter female (+ s.d.) 0.582 + 0.060 0.621 + 0.207 + + 0.737 + 0.230 0.618 + 0.190 ++ ++

to survive during non- breeding season

Missing parameter Realistic range Realistic range Probability...

pSurvWinterjuvenile 0.20-0.57 0.06-0.44 to survive before first breeding

Determinate parameters (for both scenarios)

Capacity 500 Max. number of territories

StartSize 400 Number of individuals at initialisation

MaxAge 10 Maximum age

4.1.3 (iii) Identification of pattern

As patterns to estimate pre-breeding survival, we selected variables available in the data set of empirical investigations that are influenced by several processes of the population dynamics, inclu- ding pre-breeding survival. We decided to use more than one of such patterns, since the reliability of the determined value is higher, if the model is able to reproduce multiple patterns (Wiegand et al. 2003). The selected patterns and their relation to pre-breeding survival is described below:

Chapter III · Model structure

1. Sex ratio – calculated by log(adult males/adult females): proportion of surviving fledglings